The radius of the 2nd orbit of Li2+ is x. The expected radius of the 3rd orbit of Be3+ is94x49x2716x1627x

The radius of an orbit in a hydrogen-like atom (an atom with only one electron) is given by the formula:

r = 0.529 * n^2/Z Å

where:

• r is the radius of the orbit,
• n is the principal quantum number (the number of the orbit, starting from 1),
• Z is the atomic number (the number of protons in the nucleus), and
• 0.529 Å is the radius of the first orbit in the hydrogen atom (the Bohr radius).

In the case of Li2+, Z = 3 (because lithium has 3 protons), and for the 2nd orbit, n = 2. So, the radius of the 2nd orbit of Li2+ is:

r(Li2+, n=2) = 0.529 * 2^2/3 = x (given)

For Be3+, Z = 4 (because beryllium has 4 protons), and for the 3rd orbit, n = 3. So, the radius of the 3rd orbit of Be3+ is:

r(Be3+, n=3) = 0.529 * 3^2/4

We want to find the ratio r(Be3+, n=3) / r(Li2+, n=2), which is:

r(Be3+, n=3) / r(Li2+, n=2) = (0.529 * 3^2/4) / (0.529 * 2^2/3) = (9/4) / (4/3) = 27/16

So, the expected radius of the 3rd orbit of Be3+ is 27/16 times the radius of the 2nd orbit of Li2+.